If we have the same (or more) number of equations as we do pronumerals, we should be able to evaluate the pronumerals.

Topic: simultaneous equations

If you have the same number of equations as pronumerals, it must be possible to evaluate the pronumerals

Topics: algebra, simultaneous equations

Whenever you have the same number of unknowns as you do equations it should be possible to find the unkowns. (ssuming none of the equations is a multiple of another).

Topics: algebra, simultaneous equations

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31

Nov 22, 2016
11/16

by
Iaset Journal

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In such models the emphasis was on estimating and/or predicting the average value of Y conditional upon the fixed values of the X variables. But in many situations, such a one-way or unidirectional cause-and-effect relationship is not meaningful. This occurs if Y is determined by the Xâ€™s, and some of the Xâ€™s are, in turn, determined by Y. From that caused will be occurs problem in the estimation by use the OLS and the result not good to present the relationships between them, and we can't...

Topics: Econometrics, Simultaneous Equations, Market System

Journal of Research of the National Bureau of Standards

Topics: Runge-Kutta method, simultaneous equations, missile simulations

W.F. Sheppard From Determinant to Tensor Oxford University Press 1923 Acrobat 7 Pdf 13.0 Mb. Scanned by artmisa using Canon DR2580C + flatbed option

Topics: Notation, Sets, Simultaneous Equations, Statistics, Relativity

M.V. Wilkes A Short Introduction to Numerical Analysis Cambridge University Press 1966 Acrobat 7 Pdf 3.50 Mb. Scanned by artmisa using Canon DR2580C + flatbed option

Topics: Mathematics, Iteration, Interpolation, Numerical Integration, Differentiation, ODE, Simultaneous...

In this paper, one dimensional Differential Transform Method (DTM) is applied on system of Second order differential equations. The approximate solutions obtained are in series form with easily computable components. Three examples are presented and the proximity of the numerical results obtained, when compared with exact solutions derivable from application of Laplace transform method, demonstrates the efficiency and simplicity of the method.

Topics: Differential Transform Method, Laplace Transform Method, Simultaneous equations, second order...

Topics: DTIC Archive, Neumann, Michael, CONNECTICUT UNIV STORRS DEPT OF MATHEMATICS, *SIMULTANEOUS...

When solving one equation in one unknown, f(x) = q, it is obviours geometrically that if (x) is continuously differentiable and (f'(x) not equal 0 for all x, then for each q the equation has at most one solution (f is then said to be univalent). Of course the univalence of f does not ensure the existence of a solution, for example, e to the x power = 0. When solving a system of n equations in n unknowns, fi(x1,...,xn) = qi (i = 1,...,n), the analogue of f'(x) is the n x n Jacobian matrix (del f...

Topics: DTIC Archive, Kojima,Masakazu, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER,...

The simplex method of solution of a linear program first transforms the original system to an equivalent system of m equations in canonical form by an elimination of m of the n unknowns. If the right choice of m variables is made, then by equating the remaining variables to zero, an optimal solution is obtained to the original problem. If not, the method produces an improved set of m variables and a corresponding canonical form. The procedure is iterated until an optimum solution is obtained.

Topics: DTIC Archive, Dantzig, G B, RAND CORP SANTA MONICA CA, *SCHEDULING, ALGEBRA, LINEAR PROGRAMMING,...

Topics: DTIC Archive, Bowie, Oscar L, WATERTOWN ARSENAL LABS MA, *STRESSES, *ELASTIC PROPERTIES,...

From the bitsavers.org collection, a scanned-in computer-related document. autonetics :: recomp :: software :: Recomp Users Library :: 1101 Simultanious Equations Program for the Modified Recomp II Aug61

Topics: program, equations, recomp, simultaneous, data, enter, type, computer, switch, simultaneous...

644
644

May 27, 2011
05/11

by
Hall, Edward J.; Lynn, Sean R.; Heidegger, Nathan J.; Delaney, Robert A

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The objective of this project is to provide the capability to analyze the aerodynamic performance of the complete low pressure subsystem (LPS) of the Energy Efficient Engine (EEE). The analyses were performed using three-dimensional Navier-Stokes numerical models employing advanced clustered processor computing platforms. The analysis evaluates the impact of steady aerodynamic interaction effects between the components of the LPS at design and off-design operating conditions. Mechanical...

Topics: NUMERICAL ANALYSIS, PROBABILITY THEORY, FLUX (RATE), NEUTRONS, MONTE CARLO METHOD, LINEAR...

328
328

May 27, 2011
05/11

by
Lanford, Wade E

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The results of a static investigation conducted to measure the normal forces on the entire jet-vane assembly and the hinge moments on the jet vane produced by a paddle vane oscillating in the jet of a 1,500-pound-thrust rocket motor are presented for vane-deflection angles from -5 deg to 25 deg. A maximum average normal force of 71 pounds with a corresponding value for maximum average hinge moment of 228 inch-pounds was obtained with the maximum area of jet vane immersed at a jet-vane angle of...

Topics: BOUNDARY LAYER FLOW, VELOCITY DISTRIBUTION, DEFORMATION, MAGNETOHYDRODYNAMICS, MAGNETOHYDRODYNAMIC...

It takes of the order of N-cubed operations to solve a set of N linear equations in N unknowns. When the underlying physical problem has some time- or shift-invariance properties, the coefficient matrix is of Toeplitz (or difference or convolution) type and the equations can be with O(N-squared) operations. We have shown that with any nonsingular N x N matrix, we can associate an integer alpha between 1 and N such that it takes O(N-squared alpha operations to invert the matrix. The number alpha...

Topics: DTIC Archive, Kailath,Thomas, STANFORD UNIV CALIF INFORMATION SYSTEMS LAB, *INTEGRAL EQUATIONS,...

This report documents research in the areas of stability and performance robustness. Stability robustness in the presence of structured and unstructured uncertainty is discussed relative to nonminimum phase systems. Simultaneous stabilization under unstructured uncertainties and nonconservative stability robustness bounds are addressed. Performance robustness is discussed using the D-Stability formulation. (CP)

Topics: DTIC Archive, Yedavalli, Rama K, OHIO STATE UNIV COLUMBUS DEPT OF AEROSPACE ENGINEERING, *LINEAR...

Solving large (and sparse) system of simultaneous linear equations has been (and continues to be) a major challenging problem for many real-world engineering/science applications [1-2]. For many practical/large-scale problems, the sparse, Symmetrical and Positive Definite (SPD) system of linear equations can be conveniently represented in matrix notation as [A] {x} = {b} , where the square coefficient matrix [A] and the Right-Hand-Side (RHS) vector {b} are known. The unknown solution vector {x}...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, COEFFICIENTS, LINEAR EQUATIONS, MATRICES...

The practical application of two convergence techniques designed to increase the rate of convergence of the method of successive displacements (Gauss-Siedel) for the implicit numerical solution of the diffusion equation of transient heat transfer is investigated. A sample problem of determining the temperature distribution in a cube with a constant internal heat source and fixed boundary temperatures is solved to provide the necessary data. The results provide a theoreticas for the adapted...

Topics: DTIC Archive, Poppe, Robert T, AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH, *HEAT TRANSFER,...

This research effort is an extension of previous work in single equation system modeling of the enlisted accession and retention markets. Since the two markets are related, proper model specification leads to the use of a simultaneous systems estimator. Data to estimate the model came from the time period of October 1979 through September 1987 and was chosen based on economic and historical data availability. Four separate market equations were proposed and estimated: nonprior force accessions,...

Topics: DTIC Archive, Stone, Brice M, METRICA INC SAN ANTONIO TX, *ESTIMATES, *ENLISTED PERSONNEL,...

This final report describes an investigation of thinned array antennas with unequally spaced elements. Several approaches to array design have been explored and guide lines established for designing arrays. The design techniques reported here include statistically designed density-tapered arrays, ring arrays, and the application of dynamic programming to array theory. The statistical analysis of arrays, the investigation of arrays from an energy concept and number theory have been used to...

Topics: DTIC Archive, Sherman, J W, ADVANCED TECHNOLOGY CORP TIMONIUM MD, *COUPLED ANTENNAS, *PSEUDO RANDOM...

From the bitsavers.org collection, a scanned-in computer-related document. ibm :: 1620 :: general program library :: 5.0.040 MOSES Maximum One-Pass Simultaneous Equations Solution

Topics: program, fortran, equations, deck, dum, simultaneous, equation, subroutine, subroutines, pioneer,...

The focus of this research is to implement a Lanczos algorithm for the Control-Structure Integration (CSI) code which can exploit both parallel and vector capabilities provided by modern, high performance computers. A partial restoring orthogonality scheme is also developed and incorporated into the basic Lanczos algorithm. The numerical performance of the proposed parallel-vector Lanczos algorithm is demonstrated by solving for the frequencies and mode shapes of the Phase Zero CSI model. The...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, COMPUTER PROGRAMS, CONTROL SYSTEMS DESIGN,...

Two papers are given, their purpose being to study in detail some representative problems which occur in the study of interindustry processes. The general techniques will be those of the theory of dynamic programming. The first paper considers a simple mathematical model of the interaction of two independent industries engaged in the production of one item. For convenience, the auto and steel industries are considered. The second paper treats the problem of maximizing x sub 2 (T) given the...

Topics: DTIC Archive, BELLMAN, RICHARD, RAND CORP SANTA MONICA CA, *COMPUTER PROGRAMMING, *GAME THEORY,...

The efficiency of the Simultaneous Analysis and Design (SAND) approach in the minimum weight optimization of structural systems subject to strength and displacement constraints as well as size side constraints is investigated. SAND allows for an optimization to take place in one single operation as opposed to the more traditional and sequential Nested Analysis and Design (NAND) method, where analyses and optimizations alternate. Thus, SAND has the advantage that the stiffness matrix is never...

Topics: NASA Technical Reports Server (NTRS), DESIGN ANALYSIS, OPTIMIZATION, SEQUENTIAL ANALYSIS,...

355
355

Nov 28, 2009
11/09

by
Scoby McCurdy

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: solve, equations, equation, sum, exercise, quadratic, simplify, find, exercise book, simultaneous...

Source: http://books.google.com/books?id=USIXAAAAYAAJ&oe=UTF-8

In the paper, exact tests are proposed for testing the trend in the presence of autocorrelation and also for testing the trend and autocorrelation simultaneously in a first order Markov process. Also, the simultaneous confidence intervals associated with these tests are derived. These results are extended to a higher order Markov process.

Topics: DTIC Archive, Krishnaiah, P R, AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OH, *STATISTICAL TESTS,...

Topics: DTIC Archive, Thaler, George J, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *COMPUTER PROGRAMMING,...

FNOL3 is a Fortran IV subprogram which uses fourth order Runge-Kutta and Adams-Moulton methods to solve up to 30 ordinary differential equations with initial conditions. Options allow control of error, step-size, print frequency and integration method. There is a discussion on the integration methods and their error terms. Listings of the subprogram and sample problems and their results as run on NOL's CDC 6400 are included.

Topics: DTIC Archive, Ferguson, Ralph E, NAVAL ORDNANCE LAB WHITE OAK MD, *COMPUTER PROGRAMS, *DIFFERENTIAL...

The Nutatron gyro features an anisometric rotor which responds to torques by exhibiting minute signals at twice the rotor frequency. These signals are used to automatically compensate for the drift producing torques and as a result the Nutatron is a high performance, low cost gyro with fast reaction time. Under previous contracts, the feasibility of the concept was demonstrated and an engineering model was designed, fabricated, and tested. This report covers a phase of the instrument...

Topics: DTIC Archive, BELL AEROSPACE CO BUFFALO NY, *GAS BEARINGS, *GYROSCOPES, ALIGNMENT, DRIFT, FLOW...

The mathematical derivation for a method to determine the identities and amounts of alloys present in a flame where numerous alloys may be present is described. This method is applicable if the total number of elemental species from all alloys that may be in the flame is greater than or equal to the total number of alloys. Arranging the atomic spectral line emission equations for the elemental species as a series of simultaneous equations enables solution for identity and amount of the alloy...

Topics: NASA Technical Reports Server (NTRS), FLAMES, LINE SPECTRA, PLUMES, ROCKET ENGINES, SIMULTANEOUS...

We consider the recent algorithms for computing fixed points of zeros of continuous functions from R to the nth power to itself that are based on tracing piecewise-linear paths in triangulations. We investigate the possible savings that arise when these fixed-point algorithms with their usual triangulations are applied to computing zeros of functions f with special structure: f is either linear in certain variables, separable, or has Jacobian with small bandwidth. Each of these structures leads...

Topics: DTIC Archive, Todd,Michael J, WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER, *LINEAR...

New methods for finding the inverse of a hermitian Toepiltz matrix and the related problem of solving a system of linear equations are presented. Efficient algorithmic procedures for these methods are listed. (Author)

Topics: DTIC Archive, Gerlach,Karl, NAVAL RESEARCH LAB WASHINGTON DC, *COMPUTER PROGRAMS,...

This is a discussion of methods for describing, mathematically, flows between compartments in a multi-compartment system. We will give the con ventional theory, based on the solution of a system of linear differential equations; we will also give a theory based on probability, viewing the system as a collection of 'states' with a particle moving from statto state with certain probabilities, remaining in each state a random time with an exponential distribution. Finally, we will take still...

Topics: DTIC Archive, Marsaglia, G, BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA, *PARTICLES, *STOCHASTIC...

A technique for self-calibrating and phasing a lens-feed array antenna, while normal operation is stopped, utilizes reflected energy of a continuous and coherent wave broadcast by a transmitter through a central feed while a phase controller advances the phase angles of reciprocal phase shifters in radiation electronics of the array elements at different rates to provide a distinct frequency modulation of electromagnetic wave energy returned by reflection in one mode and leakage in another mode...

Topics: NASA Technical Reports Server (NTRS), ANTENNA ARRAYS, CALIBRATING, PHASE CONTROL, PHASED ARRAYS,...

A linearized theory for the unsteady motion of a partially cavitated flat hydrofoil in two dimensions is carried out. A second linearization procedure is used, based on ideas of Timman and Guerst, to obtain the unsteady pressure distribution around the hydrofoil and the resulting force and moment, as functions of the cavitation number and Strouhal number for given pitch and/or heave.

Topics: DTIC Archive, Steinberg, Herbert, CONTROL DATA CORP MELVILLE NY TRG DIV, *HYDROFOILS, *CAVITATION,...

The problem of minimizing a real valued function F of n variables arises in many contexts. Most methods for solving this problem have their roots in Newton's method, i.e. they are based on approximating F by a quadratic function Q. If the number of variables n is large, then Newton's method can be problematic since it requires the computation and storage of the Hessian matrix of second derivatives. Use of finite differencing and sparse matrix techniques has overcome some of these problems but...

Topics: DTIC Archive, Nash, Stephen G., STANFORD UNIV CA DEPT OF COMPUTER SCIENCE, *NUMERICAL METHODS AND...

FORTRAN coded out-of-core equation solvers that solve using direct methods symmetric banded systems of simultaneous algebraic equations. Banded, frontal and column (skyline) solvers were studied as well as solvers that can partition the working area and thus could fit into any available core. Comparison timings are presented for several typical two dimensional and three dimensional continuum type grids of elements with and without midside nodes. Extensive conclusions are also given.

Topics: NASA Technical Reports Server (NTRS), COMPUTER PROGRAMS, FINITE ELEMENT METHOD, LINEAR EQUATIONS,...

Evaluation of counterfactual queries (e.g., 'If A were true, would C have been true?') is important to fault diagnosis, planning, determination of liability, and policy analysis. We present a method for evaluating counter-factuals when the underlying causal model is represented by structural models a nonlinear generalization of the simultaneous equations models commonly used in econometrics and social sciences. This new method provides a coherent means for evaluating policies involving the...

Topics: DTIC Archive, Balke, Alexander A., CALIFORNIA UNIV LOS ANGELES COGNITIVE SYSTEMS LAB, *MODELS,...

Conditions are formulated which guarantee the existence of positive solutions for simultaneous systems on an open domain with each constant is a positive measure. The main tools used are probabilistic potential theory, Markov processes, and an iterative scheme which is not a generalization of the one used for quasi-monotone systems. Quasi-monotonicity is not assumed and new results are obtained.

Topics: DTIC Archive, Glover,Joseph, FLORIDA UNIV GAINESVILLE DEPT OF MATHEMATICS, *MARKOV PROCESSES,...

This paper aims at extending the Davies-Shanbhag (1987) result to situations covering the problems considered by Schimizu (1978, 1980), Gu and Lau (1984) and Ramachandran et al (1987). Section 2, gives the results when H is bounded and micron is replaced by a certain bounded signed measure subsuming the specialized versions of the results given earlier by Shimizu (1978) and Ramchandran et al (1987); these turn out to be also extended versions of the Choquet-Deny theorem. Section 3 considers an...

Topics: DTIC Archive, Rao, C R, PITTSBURGH UNIV PA CENTER FOR MULTIVARIATE ANALYSIS, *SIMULTANEOUS...

In this thesis, the gain of the magnetic amplifier is derived theoretically as a function of different parameters of the circuit. An experimental circuit of a series-connected magnetic amplifier with a resistive load is set up to verify the theoretical results. Starting from Kirchoff's Voltage Law and Ampere's Law applied to the circuit, with the polynomial representation of the magnetization curve of the core material, a set of equations for currents and fluxes is obtained. These equations...

Topics: DTIC Archive, Kim-Thuc, Do, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *MAGNETIC AMPLIFIERS,...

In many situations, the experimenter is interested in testing which of the variances differ significantly from others when the overall hypothesis of equality of variances is rejected. The simultaneous test procedures play an important role in these situations. Hartley considered the problem of pairwise comparisons of variances simultaneously. Gnanadesikan considered the problem of comparing several variances simultaneously against a standard one. In the present paper, test procedures are...

Topics: DTIC Archive, Krishnaiah, P R, AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OH, *STATISTICAL TESTS,...

Topics: DTIC Archive, CUNNINGHAM, W. J., YALE UNIV NEW HAVEN CT DUNHAM LAB, *NONLINEAR DIFFERENTIAL...

To solve an integer linear program, we identify particular values that the objective function can assume on feasible lattice points. Thus, we reduce the problem of finding an optimal integer solution of n dimensions to that of finding a feasible integer solution of n-1 dimensions. A Branch and Bound Method is presented to solve the latter problem for the 0-1 case.

Topics: DTIC Archive, Eto, Hajime, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *LINEAR...

540
540

Dec 1, 2009
12/09

by
James Hamblin Smith

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Book digitized by Google from the library of Oxford University and uploaded to the Internet Archive by user tpb.

Topics: vjooq, elementary, sum, shew, equation, square, term, root, square root, common factor, three...

Source: http://books.google.com/books?id=H1ADAAAAQAAJ&oe=UTF-8

158
158

Jun 1, 2011
06/11

by
Dahl, Milo D.; Hixon, Ray; Mankbadi, Reda R

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An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear...

Topics: ELASTOPLASTICITY, LINEAR EQUATIONS, BUCKLING, CYLINDRICAL BODIES, RECTANGULAR PLATES, STRESS-STRAIN...

We have elucidated the mechanisms of hydrolysis of phosphate diesters by acid and metal ion catalysis. In addition a new catalyst carrier (microgonotropens) to DNA and RNA have been invented, synthesized (patented) and the reactions with DNA studied. Such information is particularly important to those interested in the catalysis of hydrolysis of DNA and RNA.

Topics: DTIC Archive, Bruice, Thomas C., CALIFORNIA UNIV SANTA BARBARA DEPT OF CHEMISTRY, *DEOXYRIBONUCLEIC...

Iterative procedures are given for joint maximum-likelihood estimation based on singly and doubly censored samples from a normal population. The simultaneous equations yielding the maximum-likelihood estimates are obtained. Since their algebraic solution is impossible, iterative procedures are proposed which are applicable in the most general case in which both parameters are unknown and in special cases in which either of the parameters is known. The asymptotic variances and covariances are...

Topics: DTIC Archive, Harter, H L, AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OH, *MONTE CARLO METHOD,...

Steepest descent and related topics are discussed. An example is given taken from a simple rendezvous problem in control theory. The problem is one of minimizing a norm on an affine subspace. The problem here is solved in the primal.

Topics: DTIC Archive, BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA GEO-ASTRO PHYSICS LAB, *ALGEBRAIC...